S hape matching and classification using height functions
This presentation is the property of its rightful owner.
Sponsored Links
1 / 17

S hape Matching and Classification Using Height Functions PowerPoint PPT Presentation


  • 93 Views
  • Uploaded on
  • Presentation posted in: General

S hape Matching and Classification Using Height Functions. Xide Xia ENGN 2560 Advisor: Prof. Kimia Project Initial Presentation. S hape Matching:. object recognition, character recognition, medical image and protein analysis …

Download Presentation

S hape Matching and Classification Using Height Functions

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


S hape matching and classification using height functions

Shape Matching and Classification Using Height Functions

Xide Xia

ENGN 2560

Advisor: Prof. Kimia

Project Initial Presentation


S hape matching

Shape Matching:

object recognition, character recognition, medical image and protein analysis …

  • Geometric Transformations (translation, rotation, scaling, etc.)

  • Nonlinear Deformations (noise, articulation and occlusion)


Steps

Steps:

  • 1) Shape descriptor with height functions

  • 2) Similarity measure using the height descriptor


Shape descriptor with height functions

Shape descriptor with height functions:

  • A sequence of equidistant sample points X:

    X={Xi} , i=1,2,….,N

  • Tangent line Li:

    its direction is always starting from Xi-1 to Xi+1

  • Height value Hi:

    the symboled distance between the jth (j = 1,. . . ,N) sample point Xj and the tangent line Li is defined as a height value hi,j.


S hape matching and classification using height functions

(the height value of the jth sample point Xj according to the reference axis Li of the point Xi)


Descriptor hi

Descriptor Hi:

  • the direction of the reference axis Li

  • the location of the sample point Xi on the shape contour X.


S hape matching and classification using height functions

  • Smoothed height values:

F is an M *N matrix with column i being the shape descriptor Fi of the sample point Xi.


S hape matching and classification using height functions

  • Local nomalization:

Consequently, the value of each entry in the matrix F after normalization is in the interval [-1, 1].


Similarity measure using the height descriptor

Similarity measure using the height descriptor:

In shape recognition, we usually compute a shape similarity or dissimilarity (distance) to find the optimal correspondence of contour points.

Dynamic Programming (DP) algorithm to find the correspondence

The shape dissimilarity: the sum of the distances of the corresponding points.


S hape matching and classification using height functions

  • The cost (distance) of matching p and q:

  • Weight coefficient

  • Dissimilarity between the two shapes:

Given two shapes X and Y. With DP we compute an optimal correspondence x to y that the is minimal.


S hape matching and classification using height functions

Humans are generally more sensitive to contour deformations when the complexity of the contour is lower!

  • Shape complexity:

where std denotes the standard deviation.


S hape matching and classification using height functions

  • The dissimilarity or distance between two shapes X, Y normalized by their shape complexity values:

where the factor is used to avoid divide-by-zero.


Shape descriptor with height functions1

Shape descriptor with height functions:

  • A sequence of equidistant sample points X

  • Tangent line Li

  • Height value Hi

  • Smoothed height values

  • Local nomalization

Similarity measure using the height descriptor:

  • The cost (distance) of matching p and q

  • Weight coefficient

  • Dissimilarity between the two shapes

  • Shape complexity

  • Dissimilarity normalized by complexity values


Schedule

Schedule:

  • 1st week: Learn the algorithm well

  • 2nd ~3th week: Write up the codes of the shape descriptor part

  • 4th ~5th week: Write up the codes of the matching part

  • 6th~7th week: Debug and Test in different datasets, Make Comparison with other shape matching algorithm (Shock Graphs)

  • 8th week: Make conclusion, Prepare for the final presentation


S hape matching and classification using height functions

Thank you


  • Login